The circle equation 5x² + 18y² - 30x + 72y + 27 = 0 represented in standard form is (x - 3)²/18 + (y + 2)²/5 = 1
Converting the circle equation to standard form
From the question, we have the following parameters that can be used in our computation:
5x² + 18y² - 30x + 72y + 27 = 0
Rewrite as
5x² + 18y² - 30x + 72y = -27
Group the equation by the variables
5x² - 30x + 18y² + 72y = -27
So, we have
5(x² - 6x) + 18(y² + 4y) = -27
Complete the square on x and y
So, we have
5(x - 3)² + 18(y + 2)² = -27 + 45 + 72
This gives
5(x - 3)² + 18(y + 2)² = 90
Next, we divide through by 90
(x - 3)²/18 + (y + 2)²/5 = 1
Hence, the standard form is (x - 3)²/18 + (y + 2)²/5 = 1